Figure P6.34-1 shows an impulse response h[n], specified as a) Determine a...

Figure P6.34-1 shows an impulse response h[n], specified as

a) Determine a choice for h₁[n] and h₂[n] such that

h[n] = h₁[n] ∗ h₂[n],

where h₁[n] is an FIR filter and where h₂[n] = 0 for n/4 not an integer. Is h₂[n] an FIR or IIR filter?

(b) The impulse response h[n] is to be used in a downsampling system as indicated in Figure P6.34-2.

Draw a flow graph implementation of the system in Figure P6.34-2 that requires the minimum number of nonzero and nonunity coefficient multipliers. You may use unit delay elements, coefficient multipliers, adders and compressors. (Multiplication by a zero or a one does not require a multiplier.)

(c) For your system, state how many multiplications per input sample and per output sample are required, giving a brief explanation.